Vidaara.orgClass 11 · Mathematics
CodeVID-M11-05-INO-01
Linear Inequalities in One Variable — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The solution of $x+3>7$ is:
- A.$x>4$
- B.$x<4$
- C.$x>10$
- D.$x\ge4$
2.
Multiplying an inequality by a negative number:
- A.keeps the sign
- B.reverses the sign
- C.makes it zero
- D.removes it
3.
The solution of $2x\le10$ is:
- A.$x\le5$
- B.$x\ge5$
- C.$x\le20$
- D.$x<5$
4.
The solution set of $x\ge0$ is:
- A.$(-\infty,0]$
- B.$[0,\infty)$
- C.$(0,\infty)$
- D.$\mathbb{R}$
5.
The solution of $-2x>6$ is:
- A.$x>-3$
- B.$x<-3$
- C.$x>3$
- D.$x<3$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Solve $3x+5<14$.
7.
Solve $-4x\ge-12$.
8.
Solve $\dfrac{x}{2}>3$.
9.
Solve $5-x\le2$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Solve $2(x-1)
11.
Solve $\dfrac{2x-1}{3}\ge\dfrac{x+2}{2}$.
12.
Solve $3(x-2)\le5x+4$.
13.
Solve $-3\le2x-1<5$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Solve $\dfrac{2x-3}{4}+9\ge3+\dfrac{4x}{3}$ and represent the solution on a number line.
15.
A company's cost is $C=20x+4000$ and revenue $R=60x$. Find the values of $x$ for which it makes a profit.
Answer Key
Section A — Multiple Choice Questions
- (A) $x>4$
- (B) reverses the sign
- (A) $x\le5$
- (B) $[0,\infty)$
- (B) $x<-3$
Section B — Short Answer (2 marks)
- $x<3$.
- $x\le3$.
- $x>6$.
- $x\ge3$.
Section C — Short Answer (3 marks)
- $x<5$.
- $x\ge8$.
- $x\ge-5$.
- $-1\le x<3$.
Section D — Long Answer (5 marks)
- $x\le6.3$ (i.e. $x\in(-\infty,6.3]$).
- $x>100$ units.
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